Contractions of Lie algebras and algebraic groups

Dietrich Burde

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Displaying similar documents to “Contractions of Lie algebras and algebraic groups”

Deformation of Lie algebras and Lie algebras of deformations

Harald Bjar, Olav Arnfinn Laudal (1990)

Compositio Mathematica

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Left-symmetric algebras, or pre-Lie algebras in geometry and physics

Dietrich Burde (2006)

Open Mathematics

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In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs arise in many different areas of mathematics and physics. We attempt to give a survey of the fields...

Lie supergroups obtained from 3-dimensional Lie superalgebras associated to the adjoint representation and having a 2-dimensional derived ideal.

Hernández, I., Peniche, R. (2008)

International Journal of Mathematics and Mathematical Sciences

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On two theorems for flat, affine group schemes over a discrete valuation ring

Adrian Vasiu (2005)

Open Mathematics

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We include short and elementary proofs of two theorems that characterize reductive group schemes over a discrete valuation ring, in a slightly more general context.

Poisson-Lie groupoids and the contraction procedure

Kenny De Commer (2015)

Banach Center Publications

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On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures...

Classification of solvable Lie algebras.

de Graaf, W.A. (2005)

Experimental Mathematics

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A Note on Strong Lie Derived Length of Group Algebras

Francesco Catino, Ernesto Spinelli (2007)

Bollettino dell'Unione Matematica Italiana

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For a group algebra KG of a non-abelian group G over a field K of positive characteristic p we study the strong Lie derived length of the associated Lie algebra.

$ℤ$ -gradations of Lie algebras and infinitesimal generators.

Richter, David A. (1999)

Journal of Lie Theory

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Computations in finite-dimensional Lie algebras.

Cohen, A.M., de Graaf, W.A., Rónyai, L. (1997)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

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A note on 2-step subideals of Lie algebras

Ian Stewart (1973)

Compositio Mathematica

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